A335155 Start with 1; if n is in the sequence, so are n+5 and 3*n.

1, 3, 6, 8, 9, 11, 13, 14, 16, 18, 19, 21, 23, 24, 26, 27, 28, 29, 31, 32, 33, 34, 36, 37, 38, 39, 41, 42, 43, 44, 46, 47, 48, 49, 51, 52, 53, 54, 56, 57, 58, 59, 61, 62, 63, 64, 66, 67, 68, 69, 71, 72, 73, 74, 76, 77, 78, 79, 81, 82, 83, 84, 86, 87, 88, 89, 91, 92, 93, 94, 96, 97, 98, 99, 101, 102, 103, 104, 106

Offset: 1

Author

N. J. A. Sloane, Jun 05 2020

Keywords

• nonn
• easy

Comments

This is the lexicographically earliest sequence of positive numbers with the property that if n is in the sequence, so are n+5 and 3*n.

Suggested by A335365 (which is the complement).

Links

• Colin Barker, Table of n, a(n) for n = 1..1000
• Index entries for linear recurrences with constant coefficients, signature (1,0,0,1,-1).

Crossrefs

Cf. A335365.

See also A005658, A005660, A005662, etc.

Programs

PARI

Vec(x*(1 + 2*x + 3*x^2 + 2*x^3 - x^6 - x^7 + x^8 - x^10 + x^11 - x^13 + x^14 - x^15 - x^16) / ((1 - x)^2*(1 + x)*(1 + x^2)) + O(x^60)) \\ Colin Barker, Jun 07 2020

Formula

From Colin Barker, Jun 07 2020: (Start)

G.f.: x*(1 + 2*x + 3*x^2 + 2*x^3 - x^6 - x^7 + x^8 - x^10 + x^11 - x^13 + x^14 - x^15 - x^16) / ((1 - x)^2*(1 + x)*(1 + x^2)).

a(n) = a(n-1) + a(n-4) - a(n-5) for n>17.

(End)